Asymmetric fluid-structure dynamics in nanoscale imprint lithography

length between the clamped-clamped ends of the actuator since this length willvary when the actuators push and pull.ALFigure 5.3 Model of actuator for stiffness computationBeam bending equations approximate the stiffness of the distributedflexure ring for each actuation arm. Each one-third segment of the distributedflexure can be modeled as a fixed-fixed beam as shown in Figure 5.4. Equation5.4 describes the bending of a fixed-fixed beam under a vertical load.FLbhFigure 5.4 Fixed-fixed beamF192EIδz= kδzL=3[5.4]3bhwhere I = . The flexure ring is machined from 7075-T6 aluminum alloy12with a Young’s modulus, E, of 72Gpa. The median radial length of the flexurering is 3.5 inches. The flexure ring is 1 inch wide and 50 mils thick. With a total63